We study fair allocation of constrained resources, where a market designer optimizes overall welfare while maintaining group fairness. In many large-scale settings, utilities are not known in advance, but are instead observed after realizing the allocation. We therefore estimate agent utilities using machine learning. Optimizing over estimates requires trading-off between mean utilities and their predictive variances. We discuss these trade-offs under two paradigms for preference modeling -- in the stochastic optimization regime, the market designer has access to a probability distribution over utilities, and in the robust optimization regime they have access to an uncertainty set containing the true utilities with high probability. We discuss utilitarian and egalitarian welfare objectives, and we explore how to optimize for them under stochastic and robust paradigms. We demonstrate the efficacy of our approaches on three publicly available conference reviewer assignment datasets. The approaches presented enable scalable constrained resource allocation under uncertainty for many combinations of objectives and preference models.

本研究解决了不确定性条件下的资源公平分配问题，旨在优化整体福利并维持群体公平。提出了一种利用机器学习估计代理效用的创新方法，权衡平均效用与预测方差之间的关系。在随机优化和鲁棒优化的框架内探讨福利目标，研究结果表明该方法在多个现实数据集上表现出色，对不确定环境下的资源分配具有重要影响。

不确定性下公平与福利效率的约束多匹配